We understand Allardyce will be summoned to a meeting within the next two days to be given the news his contract, that has a year to run, will be terminated.
On the negativity from sections of supporters, he said: "It's my job to turn that around, get better results, get better players for Everton and play better, then those fans will enjoy their football a bit more than they are at the moment".
Allardyce appeared on Sky Sports News on Monday evening to discuss the season and he received a very, very warm welcome from host Jim White.
Sam Allardyce's acrimonious Everton reign is set to finally end this week with the club recognising his unpopularity with the fans makes his position untenable.
Allardyce watched his side beaten 3-1 at West Ham on the final day of the Premier League season, with Manuel Lanzini scoring twice at the London Stadium.
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Simply press the thumbs up if you think the player should stay, and the thumbs if you think they should pack their bags. A statement from the club at the time blamed an "unwarranted approach by a Premier League rival" for Silva as being the catalyst for the destabilisation of his tenure.
Silva's possible arrival at Everton is complicated by the fact he is still involved in a wrangle with Watford over compensation for his dismissal.
It is understood he has already spoken to both Silva and Shaktar Donetsk manager Paulo Fonseca, along with several other candidates, but has always regarded Silva as his number one choice since first trying to land him back in November.
"Whenever the board tell me what they want to do then I'll know".
The former Bolton, Blackburn, Newcastle, West Ham, Sunderland and Crystal Palace boss, who had left the England post a year earlier in disgrace, eventually agreed to an 18-month term worth a reported £6m.